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Senators passed bill that would let 9/11 victims and families to sue Saudi Arabia for its alleged involvement in the attacks

The White House opposes the legislation

Washington (CNN)In a rebuke to the White House, the Senate approved a bill Tuesday to allow victims and families of the 9/11 attacks to sue Saudi Arabia for its alleged involvement in the terrorist strikes.

The bill, which the White House opposes, House Speaker Paul Ryan expressed concerns about, and Senate Majority Leader Mitch McConnell was slow to embrace, had stalled for months. It now heads to the House.

But in the end, the bill's authors -- John Cornyn of Texas, the second ranking Senate Republican, and Chuck Schumer of New York, the third-ranking Senate Democrat -- were able to pass the bill on a voice vote, a rare feat in the divided chamber, especially for a controversial issue.

White House press secretary Josh Earnest renewed the threat that President Barack Obama will veto the bill.

"Yes, as I think I've mentioned before it's given the concerns we've expressed it's difficult to imagine the President signing this legislation and that continues to be true," Earnest told reporters.

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The White House and State Department say the bill could have dramatic ramifications for the United States and citizens living abroad to retaliatory lawsuits.

"This legislation would change long standing international law regarding sovereign immunity and the President of the United States and continues to harbor serious concerns that this legislation would make the United States vulnerable in other court systems around the world," Earnest said.

Formally known as the Justice Against Sponsors of Terrorism Act, the bill would prevent Saudi Arabia and other countries alleged to have terrorist ties from invoking their sovereign immunity in federal court.

Saudi Arabia has long denied any role in the 9/11 attacks, but victims' families have repeatedly sought to bring the matter to court, only to be rebuffed after the country has invoked legal immunity allowed under current law. In March, Saudi Foreign Minister Adel al-Jubeir warned lawmakers that it would sell $750 billion in U.S. assets, including treasury securities, should the bill become law.

Schumer, Cornyn dismiss Saudi threats

The legislation has been a major focus of 9/11 families who pushed to win the right to sue.

"These families have lit a candle. Their mission is not just to bring justice to themselves but to send a loud message to foreign governments. If you help create terrorism on American soil, you're going to be brought to justice," Schumer said at a press conference.

Cornyn and Schumer each dismissed as "hallow" threats from Saudi Arabia that it would sell off assets it holds in the U.S. if the law was changed.

"They're not going to suffer a huge financial loss just to make a point," said Cornyn who also predicted the legislation would not be "disruptive of the relationship we have with the Kingdom of Saudi Arabia."

Either way, Schumer said it was worth the risk.

"If the Saudis didn't participate in this terrorism, they have nothing to fear about going to court. If they did, they should be held accountable," the New York lawmaker who represents so many victims of 9/11.

Terry Strada, whose husband, Tom, died in the attacks, traveled from New Jersey to Washington with her daughter Caitlin as soon as they were told the vote was going to happen.

"We've waited long enough. We've waited 15 years. We shouldn't have to wait any longer," Strada told CNN. "It's good policy to hold accountable any nation that aids in a terror attack on U.S. soil and that aids in the death of U.S. citizens."

Strada says she and others are meeting Wednesday with Ryan.

"We feel that the bill is in very good position to move through the House," she said. "We are very excited finally to get it to the House."